Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

For j ≤ k, the L(j, k)-labeling arose from code assignment problem. That is, let j, k and m be positive numbers, an m-L(j, k)-labeling of a graph G is a mapping f : V(G) → [0, m] such that | f (u)− f (v)| ≥ j if d(u, v) = 1, and | f (u)− f (v)| ≥ k if d(u, v) = 2. The span of f is the difference between the maximum and the minimum numbers assigned by f . The L(j, k)-labeling number of G, denoted by λ j,k (G), is the minimum span over all L(j, k)-labelings of G. The kth power G k of an undirected graph G is the graph with the vertex set of G in which two vertices are adjacent when their distance in G is at most k. In this paper, the L(j, k)-labeling numbers of P 2 n are determined for j ≤ k.

Keywords

L(j, k)-labeling, Path, Square of path, Code assignment

Publication Date

12-2017

Source Publication Title

AKCE International Journal of Graphs and Combinatorics

Volume

14

Issue

3

Start Page

307

End Page

316

Publisher

Elsevier

Peer Reviewed

1

Copyright

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Funder

Open Access funded by Kalasalingam University

DOI

10.1016/j.akcej.2017.07.001

Link to Publisher's Edition

http://dx.doi.org/10.1016/j.akcej.2017.07.001

ISSN (print)

09728600

Included in

Mathematics Commons

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